Traktor/myenv/Lib/site-packages/matplotlib/tests/test_mlab.py

1023 lines
41 KiB
Python
Raw Normal View History

2024-05-23 01:57:24 +02:00
from numpy.testing import (assert_allclose, assert_almost_equal,
assert_array_equal, assert_array_almost_equal_nulp)
import numpy as np
import pytest
from matplotlib import mlab
def test_window():
np.random.seed(0)
n = 1000
rand = np.random.standard_normal(n) + 100
ones = np.ones(n)
assert_array_equal(mlab.window_none(ones), ones)
assert_array_equal(mlab.window_none(rand), rand)
assert_array_equal(np.hanning(len(rand)) * rand, mlab.window_hanning(rand))
assert_array_equal(np.hanning(len(ones)), mlab.window_hanning(ones))
class TestDetrend:
def setup_method(self):
np.random.seed(0)
n = 1000
x = np.linspace(0., 100, n)
self.sig_zeros = np.zeros(n)
self.sig_off = self.sig_zeros + 100.
self.sig_slope = np.linspace(-10., 90., n)
self.sig_slope_mean = x - x.mean()
self.sig_base = (
np.random.standard_normal(n) + np.sin(x*2*np.pi/(n/100)))
self.sig_base -= self.sig_base.mean()
def allclose(self, *args):
assert_allclose(*args, atol=1e-8)
def test_detrend_none(self):
assert mlab.detrend_none(0.) == 0.
assert mlab.detrend_none(0., axis=1) == 0.
assert mlab.detrend(0., key="none") == 0.
assert mlab.detrend(0., key=mlab.detrend_none) == 0.
for sig in [
5.5, self.sig_off, self.sig_slope, self.sig_base,
(self.sig_base + self.sig_slope + self.sig_off).tolist(),
np.vstack([self.sig_base, # 2D case.
self.sig_base + self.sig_off,
self.sig_base + self.sig_slope,
self.sig_base + self.sig_off + self.sig_slope]),
np.vstack([self.sig_base, # 2D transposed case.
self.sig_base + self.sig_off,
self.sig_base + self.sig_slope,
self.sig_base + self.sig_off + self.sig_slope]).T,
]:
if isinstance(sig, np.ndarray):
assert_array_equal(mlab.detrend_none(sig), sig)
else:
assert mlab.detrend_none(sig) == sig
def test_detrend_mean(self):
for sig in [0., 5.5]: # 0D.
assert mlab.detrend_mean(sig) == 0.
assert mlab.detrend(sig, key="mean") == 0.
assert mlab.detrend(sig, key=mlab.detrend_mean) == 0.
# 1D.
self.allclose(mlab.detrend_mean(self.sig_zeros), self.sig_zeros)
self.allclose(mlab.detrend_mean(self.sig_base), self.sig_base)
self.allclose(mlab.detrend_mean(self.sig_base + self.sig_off),
self.sig_base)
self.allclose(mlab.detrend_mean(self.sig_base + self.sig_slope),
self.sig_base + self.sig_slope_mean)
self.allclose(
mlab.detrend_mean(self.sig_base + self.sig_slope + self.sig_off),
self.sig_base + self.sig_slope_mean)
def test_detrend_mean_1d_base_slope_off_list_andor_axis0(self):
input = self.sig_base + self.sig_slope + self.sig_off
target = self.sig_base + self.sig_slope_mean
self.allclose(mlab.detrend_mean(input, axis=0), target)
self.allclose(mlab.detrend_mean(input.tolist()), target)
self.allclose(mlab.detrend_mean(input.tolist(), axis=0), target)
def test_detrend_mean_2d(self):
input = np.vstack([self.sig_off,
self.sig_base + self.sig_off])
target = np.vstack([self.sig_zeros,
self.sig_base])
self.allclose(mlab.detrend_mean(input), target)
self.allclose(mlab.detrend_mean(input, axis=None), target)
self.allclose(mlab.detrend_mean(input.T, axis=None).T, target)
self.allclose(mlab.detrend(input), target)
self.allclose(mlab.detrend(input, axis=None), target)
self.allclose(
mlab.detrend(input.T, key="constant", axis=None), target.T)
input = np.vstack([self.sig_base,
self.sig_base + self.sig_off,
self.sig_base + self.sig_slope,
self.sig_base + self.sig_off + self.sig_slope])
target = np.vstack([self.sig_base,
self.sig_base,
self.sig_base + self.sig_slope_mean,
self.sig_base + self.sig_slope_mean])
self.allclose(mlab.detrend_mean(input.T, axis=0), target.T)
self.allclose(mlab.detrend_mean(input, axis=1), target)
self.allclose(mlab.detrend_mean(input, axis=-1), target)
self.allclose(mlab.detrend(input, key="default", axis=1), target)
self.allclose(mlab.detrend(input.T, key="mean", axis=0), target.T)
self.allclose(
mlab.detrend(input.T, key=mlab.detrend_mean, axis=0), target.T)
def test_detrend_ValueError(self):
for signal, kwargs in [
(self.sig_slope[np.newaxis], {"key": "spam"}),
(self.sig_slope[np.newaxis], {"key": 5}),
(5.5, {"axis": 0}),
(self.sig_slope, {"axis": 1}),
(self.sig_slope[np.newaxis], {"axis": 2}),
]:
with pytest.raises(ValueError):
mlab.detrend(signal, **kwargs)
def test_detrend_mean_ValueError(self):
for signal, kwargs in [
(5.5, {"axis": 0}),
(self.sig_slope, {"axis": 1}),
(self.sig_slope[np.newaxis], {"axis": 2}),
]:
with pytest.raises(ValueError):
mlab.detrend_mean(signal, **kwargs)
def test_detrend_linear(self):
# 0D.
assert mlab.detrend_linear(0.) == 0.
assert mlab.detrend_linear(5.5) == 0.
assert mlab.detrend(5.5, key="linear") == 0.
assert mlab.detrend(5.5, key=mlab.detrend_linear) == 0.
for sig in [ # 1D.
self.sig_off,
self.sig_slope,
self.sig_slope + self.sig_off,
]:
self.allclose(mlab.detrend_linear(sig), self.sig_zeros)
def test_detrend_str_linear_1d(self):
input = self.sig_slope + self.sig_off
target = self.sig_zeros
self.allclose(mlab.detrend(input, key="linear"), target)
self.allclose(mlab.detrend(input, key=mlab.detrend_linear), target)
self.allclose(mlab.detrend_linear(input.tolist()), target)
def test_detrend_linear_2d(self):
input = np.vstack([self.sig_off,
self.sig_slope,
self.sig_slope + self.sig_off])
target = np.vstack([self.sig_zeros,
self.sig_zeros,
self.sig_zeros])
self.allclose(
mlab.detrend(input.T, key="linear", axis=0), target.T)
self.allclose(
mlab.detrend(input.T, key=mlab.detrend_linear, axis=0), target.T)
self.allclose(
mlab.detrend(input, key="linear", axis=1), target)
self.allclose(
mlab.detrend(input, key=mlab.detrend_linear, axis=1), target)
with pytest.raises(ValueError):
mlab.detrend_linear(self.sig_slope[np.newaxis])
@pytest.mark.parametrize('iscomplex', [False, True],
ids=['real', 'complex'], scope='class')
@pytest.mark.parametrize('sides', ['onesided', 'twosided', 'default'],
scope='class')
@pytest.mark.parametrize(
'fstims,len_x,NFFT_density,nover_density,pad_to_density,pad_to_spectrum',
[
([], None, -1, -1, -1, -1),
([4], None, -1, -1, -1, -1),
([4, 5, 10], None, -1, -1, -1, -1),
([], None, None, -1, -1, None),
([], None, -1, -1, None, None),
([], None, None, -1, None, None),
([], 1024, 512, -1, -1, 128),
([], 256, -1, -1, 33, 257),
([], 255, 33, -1, -1, None),
([], 256, 128, -1, 256, 256),
([], None, -1, 32, -1, -1),
],
ids=[
'nosig',
'Fs4',
'FsAll',
'nosig_noNFFT',
'nosig_nopad_to',
'nosig_noNFFT_no_pad_to',
'nosig_trim',
'nosig_odd',
'nosig_oddlen',
'nosig_stretch',
'nosig_overlap',
],
scope='class')
class TestSpectral:
@pytest.fixture(scope='class', autouse=True)
def stim(self, request, fstims, iscomplex, sides, len_x, NFFT_density,
nover_density, pad_to_density, pad_to_spectrum):
Fs = 100.
x = np.arange(0, 10, 1 / Fs)
if len_x is not None:
x = x[:len_x]
# get the stimulus frequencies, defaulting to None
fstims = [Fs / fstim for fstim in fstims]
# get the constants, default to calculated values
if NFFT_density is None:
NFFT_density_real = 256
elif NFFT_density < 0:
NFFT_density_real = NFFT_density = 100
else:
NFFT_density_real = NFFT_density
if nover_density is None:
nover_density_real = 0
elif nover_density < 0:
nover_density_real = nover_density = NFFT_density_real // 2
else:
nover_density_real = nover_density
if pad_to_density is None:
pad_to_density_real = NFFT_density_real
elif pad_to_density < 0:
pad_to_density = int(2**np.ceil(np.log2(NFFT_density_real)))
pad_to_density_real = pad_to_density
else:
pad_to_density_real = pad_to_density
if pad_to_spectrum is None:
pad_to_spectrum_real = len(x)
elif pad_to_spectrum < 0:
pad_to_spectrum_real = pad_to_spectrum = len(x)
else:
pad_to_spectrum_real = pad_to_spectrum
if pad_to_spectrum is None:
NFFT_spectrum_real = NFFT_spectrum = pad_to_spectrum_real
else:
NFFT_spectrum_real = NFFT_spectrum = len(x)
nover_spectrum = 0
NFFT_specgram = NFFT_density
nover_specgram = nover_density
pad_to_specgram = pad_to_density
NFFT_specgram_real = NFFT_density_real
nover_specgram_real = nover_density_real
if sides == 'onesided' or (sides == 'default' and not iscomplex):
# frequencies for specgram, psd, and csd
# need to handle even and odd differently
if pad_to_density_real % 2:
freqs_density = np.linspace(0, Fs / 2,
num=pad_to_density_real,
endpoint=False)[::2]
else:
freqs_density = np.linspace(0, Fs / 2,
num=pad_to_density_real // 2 + 1)
# frequencies for complex, magnitude, angle, and phase spectrums
# need to handle even and odd differently
if pad_to_spectrum_real % 2:
freqs_spectrum = np.linspace(0, Fs / 2,
num=pad_to_spectrum_real,
endpoint=False)[::2]
else:
freqs_spectrum = np.linspace(0, Fs / 2,
num=pad_to_spectrum_real // 2 + 1)
else:
# frequencies for specgram, psd, and csd
# need to handle even and odd differently
if pad_to_density_real % 2:
freqs_density = np.linspace(-Fs / 2, Fs / 2,
num=2 * pad_to_density_real,
endpoint=False)[1::2]
else:
freqs_density = np.linspace(-Fs / 2, Fs / 2,
num=pad_to_density_real,
endpoint=False)
# frequencies for complex, magnitude, angle, and phase spectrums
# need to handle even and odd differently
if pad_to_spectrum_real % 2:
freqs_spectrum = np.linspace(-Fs / 2, Fs / 2,
num=2 * pad_to_spectrum_real,
endpoint=False)[1::2]
else:
freqs_spectrum = np.linspace(-Fs / 2, Fs / 2,
num=pad_to_spectrum_real,
endpoint=False)
freqs_specgram = freqs_density
# time points for specgram
t_start = NFFT_specgram_real // 2
t_stop = len(x) - NFFT_specgram_real // 2 + 1
t_step = NFFT_specgram_real - nover_specgram_real
t_specgram = x[t_start:t_stop:t_step]
if NFFT_specgram_real % 2:
t_specgram += 1 / Fs / 2
if len(t_specgram) == 0:
t_specgram = np.array([NFFT_specgram_real / (2 * Fs)])
t_spectrum = np.array([NFFT_spectrum_real / (2 * Fs)])
t_density = t_specgram
y = np.zeros_like(x)
for i, fstim in enumerate(fstims):
y += np.sin(fstim * x * np.pi * 2) * 10**i
if iscomplex:
y = y.astype('complex')
# Interestingly, the instance on which this fixture is called is not
# the same as the one on which a test is run. So we need to modify the
# class itself when using a class-scoped fixture.
cls = request.cls
cls.Fs = Fs
cls.sides = sides
cls.fstims = fstims
cls.NFFT_density = NFFT_density
cls.nover_density = nover_density
cls.pad_to_density = pad_to_density
cls.NFFT_spectrum = NFFT_spectrum
cls.nover_spectrum = nover_spectrum
cls.pad_to_spectrum = pad_to_spectrum
cls.NFFT_specgram = NFFT_specgram
cls.nover_specgram = nover_specgram
cls.pad_to_specgram = pad_to_specgram
cls.t_specgram = t_specgram
cls.t_density = t_density
cls.t_spectrum = t_spectrum
cls.y = y
cls.freqs_density = freqs_density
cls.freqs_spectrum = freqs_spectrum
cls.freqs_specgram = freqs_specgram
cls.NFFT_density_real = NFFT_density_real
def check_freqs(self, vals, targfreqs, resfreqs, fstims):
assert resfreqs.argmin() == 0
assert resfreqs.argmax() == len(resfreqs)-1
assert_allclose(resfreqs, targfreqs, atol=1e-06)
for fstim in fstims:
i = np.abs(resfreqs - fstim).argmin()
assert vals[i] > vals[i+2]
assert vals[i] > vals[i-2]
def check_maxfreq(self, spec, fsp, fstims):
# skip the test if there are no frequencies
if len(fstims) == 0:
return
# if twosided, do the test for each side
if fsp.min() < 0:
fspa = np.abs(fsp)
zeroind = fspa.argmin()
self.check_maxfreq(spec[:zeroind], fspa[:zeroind], fstims)
self.check_maxfreq(spec[zeroind:], fspa[zeroind:], fstims)
return
fstimst = fstims[:]
spect = spec.copy()
# go through each peak and make sure it is correctly the maximum peak
while fstimst:
maxind = spect.argmax()
maxfreq = fsp[maxind]
assert_almost_equal(maxfreq, fstimst[-1])
del fstimst[-1]
spect[maxind-5:maxind+5] = 0
def test_spectral_helper_raises(self):
# We don't use parametrize here to handle ``y = self.y``.
for kwargs in [ # Various error conditions:
{"y": self.y+1, "mode": "complex"}, # Modes requiring ``x is y``.
{"y": self.y+1, "mode": "magnitude"},
{"y": self.y+1, "mode": "angle"},
{"y": self.y+1, "mode": "phase"},
{"mode": "spam"}, # Bad mode.
{"y": self.y, "sides": "eggs"}, # Bad sides.
{"y": self.y, "NFFT": 10, "noverlap": 20}, # noverlap > NFFT.
{"NFFT": 10, "noverlap": 10}, # noverlap == NFFT.
{"y": self.y, "NFFT": 10,
"window": np.ones(9)}, # len(win) != NFFT.
]:
with pytest.raises(ValueError):
mlab._spectral_helper(x=self.y, **kwargs)
@pytest.mark.parametrize('mode', ['default', 'psd'])
def test_single_spectrum_helper_unsupported_modes(self, mode):
with pytest.raises(ValueError):
mlab._single_spectrum_helper(x=self.y, mode=mode)
@pytest.mark.parametrize("mode, case", [
("psd", "density"),
("magnitude", "specgram"),
("magnitude", "spectrum"),
])
def test_spectral_helper_psd(self, mode, case):
freqs = getattr(self, f"freqs_{case}")
spec, fsp, t = mlab._spectral_helper(
x=self.y, y=self.y,
NFFT=getattr(self, f"NFFT_{case}"),
Fs=self.Fs,
noverlap=getattr(self, f"nover_{case}"),
pad_to=getattr(self, f"pad_to_{case}"),
sides=self.sides,
mode=mode)
assert_allclose(fsp, freqs, atol=1e-06)
assert_allclose(t, getattr(self, f"t_{case}"), atol=1e-06)
assert spec.shape[0] == freqs.shape[0]
assert spec.shape[1] == getattr(self, f"t_{case}").shape[0]
def test_csd(self):
freqs = self.freqs_density
spec, fsp = mlab.csd(x=self.y, y=self.y+1,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=self.nover_density,
pad_to=self.pad_to_density,
sides=self.sides)
assert_allclose(fsp, freqs, atol=1e-06)
assert spec.shape == freqs.shape
def test_csd_padding(self):
"""Test zero padding of csd()."""
if self.NFFT_density is None: # for derived classes
return
sargs = dict(x=self.y, y=self.y+1, Fs=self.Fs, window=mlab.window_none,
sides=self.sides)
spec0, _ = mlab.csd(NFFT=self.NFFT_density, **sargs)
spec1, _ = mlab.csd(NFFT=self.NFFT_density*2, **sargs)
assert_almost_equal(np.sum(np.conjugate(spec0)*spec0).real,
np.sum(np.conjugate(spec1/2)*spec1/2).real)
def test_psd(self):
freqs = self.freqs_density
spec, fsp = mlab.psd(x=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=self.nover_density,
pad_to=self.pad_to_density,
sides=self.sides)
assert spec.shape == freqs.shape
self.check_freqs(spec, freqs, fsp, self.fstims)
@pytest.mark.parametrize(
'make_data, detrend',
[(np.zeros, mlab.detrend_mean), (np.zeros, 'mean'),
(np.arange, mlab.detrend_linear), (np.arange, 'linear')])
def test_psd_detrend(self, make_data, detrend):
if self.NFFT_density is None:
return
ydata = make_data(self.NFFT_density)
ydata1 = ydata+5
ydata2 = ydata+3.3
ydata = np.vstack([ydata1, ydata2])
ydata = np.tile(ydata, (20, 1))
ydatab = ydata.T.flatten()
ydata = ydata.flatten()
ycontrol = np.zeros_like(ydata)
spec_g, fsp_g = mlab.psd(x=ydata,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides,
detrend=detrend)
spec_b, fsp_b = mlab.psd(x=ydatab,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides,
detrend=detrend)
spec_c, fsp_c = mlab.psd(x=ycontrol,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides)
assert_array_equal(fsp_g, fsp_c)
assert_array_equal(fsp_b, fsp_c)
assert_allclose(spec_g, spec_c, atol=1e-08)
# these should not be almost equal
with pytest.raises(AssertionError):
assert_allclose(spec_b, spec_c, atol=1e-08)
def test_psd_window_hanning(self):
if self.NFFT_density is None:
return
ydata = np.arange(self.NFFT_density)
ydata1 = ydata+5
ydata2 = ydata+3.3
windowVals = mlab.window_hanning(np.ones_like(ydata1))
ycontrol1 = ydata1 * windowVals
ycontrol2 = mlab.window_hanning(ydata2)
ydata = np.vstack([ydata1, ydata2])
ycontrol = np.vstack([ycontrol1, ycontrol2])
ydata = np.tile(ydata, (20, 1))
ycontrol = np.tile(ycontrol, (20, 1))
ydatab = ydata.T.flatten()
ydataf = ydata.flatten()
ycontrol = ycontrol.flatten()
spec_g, fsp_g = mlab.psd(x=ydataf,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides,
window=mlab.window_hanning)
spec_b, fsp_b = mlab.psd(x=ydatab,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides,
window=mlab.window_hanning)
spec_c, fsp_c = mlab.psd(x=ycontrol,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides,
window=mlab.window_none)
spec_c *= len(ycontrol1)/(windowVals**2).sum()
assert_array_equal(fsp_g, fsp_c)
assert_array_equal(fsp_b, fsp_c)
assert_allclose(spec_g, spec_c, atol=1e-08)
# these should not be almost equal
with pytest.raises(AssertionError):
assert_allclose(spec_b, spec_c, atol=1e-08)
def test_psd_window_hanning_detrend_linear(self):
if self.NFFT_density is None:
return
ydata = np.arange(self.NFFT_density)
ycontrol = np.zeros(self.NFFT_density)
ydata1 = ydata+5
ydata2 = ydata+3.3
ycontrol1 = ycontrol
ycontrol2 = ycontrol
windowVals = mlab.window_hanning(np.ones_like(ycontrol1))
ycontrol1 = ycontrol1 * windowVals
ycontrol2 = mlab.window_hanning(ycontrol2)
ydata = np.vstack([ydata1, ydata2])
ycontrol = np.vstack([ycontrol1, ycontrol2])
ydata = np.tile(ydata, (20, 1))
ycontrol = np.tile(ycontrol, (20, 1))
ydatab = ydata.T.flatten()
ydataf = ydata.flatten()
ycontrol = ycontrol.flatten()
spec_g, fsp_g = mlab.psd(x=ydataf,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides,
detrend=mlab.detrend_linear,
window=mlab.window_hanning)
spec_b, fsp_b = mlab.psd(x=ydatab,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides,
detrend=mlab.detrend_linear,
window=mlab.window_hanning)
spec_c, fsp_c = mlab.psd(x=ycontrol,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides,
window=mlab.window_none)
spec_c *= len(ycontrol1)/(windowVals**2).sum()
assert_array_equal(fsp_g, fsp_c)
assert_array_equal(fsp_b, fsp_c)
assert_allclose(spec_g, spec_c, atol=1e-08)
# these should not be almost equal
with pytest.raises(AssertionError):
assert_allclose(spec_b, spec_c, atol=1e-08)
def test_psd_window_flattop(self):
# flattop window
# adaption from https://github.com/scipy/scipy/blob\
# /v1.10.0/scipy/signal/windows/_windows.py#L562-L622
a = [0.21557895, 0.41663158, 0.277263158, 0.083578947, 0.006947368]
fac = np.linspace(-np.pi, np.pi, self.NFFT_density_real)
win = np.zeros(self.NFFT_density_real)
for k in range(len(a)):
win += a[k] * np.cos(k * fac)
spec, fsp = mlab.psd(x=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides,
window=win,
scale_by_freq=False)
spec_a, fsp_a = mlab.psd(x=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=0,
sides=self.sides,
window=win)
assert_allclose(spec*win.sum()**2,
spec_a*self.Fs*(win**2).sum(),
atol=1e-08)
def test_psd_windowarray(self):
freqs = self.freqs_density
spec, fsp = mlab.psd(x=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=self.nover_density,
pad_to=self.pad_to_density,
sides=self.sides,
window=np.ones(self.NFFT_density_real))
assert_allclose(fsp, freqs, atol=1e-06)
assert spec.shape == freqs.shape
def test_psd_windowarray_scale_by_freq(self):
win = mlab.window_hanning(np.ones(self.NFFT_density_real))
spec, fsp = mlab.psd(x=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=self.nover_density,
pad_to=self.pad_to_density,
sides=self.sides,
window=mlab.window_hanning)
spec_s, fsp_s = mlab.psd(x=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=self.nover_density,
pad_to=self.pad_to_density,
sides=self.sides,
window=mlab.window_hanning,
scale_by_freq=True)
spec_n, fsp_n = mlab.psd(x=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=self.nover_density,
pad_to=self.pad_to_density,
sides=self.sides,
window=mlab.window_hanning,
scale_by_freq=False)
assert_array_equal(fsp, fsp_s)
assert_array_equal(fsp, fsp_n)
assert_array_equal(spec, spec_s)
assert_allclose(spec_s*(win**2).sum(),
spec_n/self.Fs*win.sum()**2,
atol=1e-08)
@pytest.mark.parametrize(
"kind", ["complex", "magnitude", "angle", "phase"])
def test_spectrum(self, kind):
freqs = self.freqs_spectrum
spec, fsp = getattr(mlab, f"{kind}_spectrum")(
x=self.y,
Fs=self.Fs, sides=self.sides, pad_to=self.pad_to_spectrum)
assert_allclose(fsp, freqs, atol=1e-06)
assert spec.shape == freqs.shape
if kind == "magnitude":
self.check_maxfreq(spec, fsp, self.fstims)
self.check_freqs(spec, freqs, fsp, self.fstims)
@pytest.mark.parametrize(
'kwargs',
[{}, {'mode': 'default'}, {'mode': 'psd'}, {'mode': 'magnitude'},
{'mode': 'complex'}, {'mode': 'angle'}, {'mode': 'phase'}])
def test_specgram(self, kwargs):
freqs = self.freqs_specgram
spec, fsp, t = mlab.specgram(x=self.y,
NFFT=self.NFFT_specgram,
Fs=self.Fs,
noverlap=self.nover_specgram,
pad_to=self.pad_to_specgram,
sides=self.sides,
**kwargs)
if kwargs.get('mode') == 'complex':
spec = np.abs(spec)
specm = np.mean(spec, axis=1)
assert_allclose(fsp, freqs, atol=1e-06)
assert_allclose(t, self.t_specgram, atol=1e-06)
assert spec.shape[0] == freqs.shape[0]
assert spec.shape[1] == self.t_specgram.shape[0]
if kwargs.get('mode') not in ['complex', 'angle', 'phase']:
# using a single freq, so all time slices should be about the same
if np.abs(spec.max()) != 0:
assert_allclose(
np.diff(spec, axis=1).max() / np.abs(spec.max()), 0,
atol=1e-02)
if kwargs.get('mode') not in ['angle', 'phase']:
self.check_freqs(specm, freqs, fsp, self.fstims)
def test_specgram_warn_only1seg(self):
"""Warning should be raised if len(x) <= NFFT."""
with pytest.warns(UserWarning, match="Only one segment is calculated"):
mlab.specgram(x=self.y, NFFT=len(self.y), Fs=self.Fs)
def test_psd_csd_equal(self):
Pxx, freqsxx = mlab.psd(x=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=self.nover_density,
pad_to=self.pad_to_density,
sides=self.sides)
Pxy, freqsxy = mlab.csd(x=self.y, y=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=self.nover_density,
pad_to=self.pad_to_density,
sides=self.sides)
assert_array_almost_equal_nulp(Pxx, Pxy)
assert_array_equal(freqsxx, freqsxy)
@pytest.mark.parametrize("mode", ["default", "psd"])
def test_specgram_auto_default_psd_equal(self, mode):
"""
Test that mlab.specgram without mode and with mode 'default' and 'psd'
are all the same.
"""
speca, freqspeca, ta = mlab.specgram(x=self.y,
NFFT=self.NFFT_specgram,
Fs=self.Fs,
noverlap=self.nover_specgram,
pad_to=self.pad_to_specgram,
sides=self.sides)
specb, freqspecb, tb = mlab.specgram(x=self.y,
NFFT=self.NFFT_specgram,
Fs=self.Fs,
noverlap=self.nover_specgram,
pad_to=self.pad_to_specgram,
sides=self.sides,
mode=mode)
assert_array_equal(speca, specb)
assert_array_equal(freqspeca, freqspecb)
assert_array_equal(ta, tb)
@pytest.mark.parametrize(
"mode, conv", [
("magnitude", np.abs),
("angle", np.angle),
("phase", lambda x: np.unwrap(np.angle(x), axis=0))
])
def test_specgram_complex_equivalent(self, mode, conv):
specc, freqspecc, tc = mlab.specgram(x=self.y,
NFFT=self.NFFT_specgram,
Fs=self.Fs,
noverlap=self.nover_specgram,
pad_to=self.pad_to_specgram,
sides=self.sides,
mode='complex')
specm, freqspecm, tm = mlab.specgram(x=self.y,
NFFT=self.NFFT_specgram,
Fs=self.Fs,
noverlap=self.nover_specgram,
pad_to=self.pad_to_specgram,
sides=self.sides,
mode=mode)
assert_array_equal(freqspecc, freqspecm)
assert_array_equal(tc, tm)
assert_allclose(conv(specc), specm, atol=1e-06)
def test_psd_windowarray_equal(self):
win = mlab.window_hanning(np.ones(self.NFFT_density_real))
speca, fspa = mlab.psd(x=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=self.nover_density,
pad_to=self.pad_to_density,
sides=self.sides,
window=win)
specb, fspb = mlab.psd(x=self.y,
NFFT=self.NFFT_density,
Fs=self.Fs,
noverlap=self.nover_density,
pad_to=self.pad_to_density,
sides=self.sides)
assert_array_equal(fspa, fspb)
assert_allclose(speca, specb, atol=1e-08)
# extra test for cohere...
def test_cohere():
N = 1024
np.random.seed(19680801)
x = np.random.randn(N)
# phase offset
y = np.roll(x, 20)
# high-freq roll-off
y = np.convolve(y, np.ones(20) / 20., mode='same')
cohsq, f = mlab.cohere(x, y, NFFT=256, Fs=2, noverlap=128)
assert_allclose(np.mean(cohsq), 0.837, atol=1.e-3)
assert np.isreal(np.mean(cohsq))
# *****************************************************************
# These Tests were taken from SCIPY with some minor modifications
# this can be retrieved from:
# https://github.com/scipy/scipy/blob/master/scipy/stats/tests/test_kdeoth.py
# *****************************************************************
class TestGaussianKDE:
def test_kde_integer_input(self):
"""Regression test for #1181."""
x1 = np.arange(5)
kde = mlab.GaussianKDE(x1)
y_expected = [0.13480721, 0.18222869, 0.19514935, 0.18222869,
0.13480721]
np.testing.assert_array_almost_equal(kde(x1), y_expected, decimal=6)
def test_gaussian_kde_covariance_caching(self):
x1 = np.array([-7, -5, 1, 4, 5], dtype=float)
xs = np.linspace(-10, 10, num=5)
# These expected values are from scipy 0.10, before some changes to
# gaussian_kde. They were not compared with any external reference.
y_expected = [0.02463386, 0.04689208, 0.05395444, 0.05337754,
0.01664475]
# set it to the default bandwidth.
kde2 = mlab.GaussianKDE(x1, 'scott')
y2 = kde2(xs)
np.testing.assert_array_almost_equal(y_expected, y2, decimal=7)
def test_kde_bandwidth_method(self):
np.random.seed(8765678)
n_basesample = 50
xn = np.random.randn(n_basesample)
# Default
gkde = mlab.GaussianKDE(xn)
# Supply a callable
gkde2 = mlab.GaussianKDE(xn, 'scott')
# Supply a scalar
gkde3 = mlab.GaussianKDE(xn, bw_method=gkde.factor)
xs = np.linspace(-7, 7, 51)
kdepdf = gkde.evaluate(xs)
kdepdf2 = gkde2.evaluate(xs)
assert kdepdf.all() == kdepdf2.all()
kdepdf3 = gkde3.evaluate(xs)
assert kdepdf.all() == kdepdf3.all()
class TestGaussianKDECustom:
def test_no_data(self):
"""Pass no data into the GaussianKDE class."""
with pytest.raises(ValueError):
mlab.GaussianKDE([])
def test_single_dataset_element(self):
"""Pass a single dataset element into the GaussianKDE class."""
with pytest.raises(ValueError):
mlab.GaussianKDE([42])
def test_silverman_multidim_dataset(self):
"""Test silverman's for a multi-dimensional array."""
x1 = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
with pytest.raises(np.linalg.LinAlgError):
mlab.GaussianKDE(x1, "silverman")
def test_silverman_singledim_dataset(self):
"""Test silverman's output for a single dimension list."""
x1 = np.array([-7, -5, 1, 4, 5])
mygauss = mlab.GaussianKDE(x1, "silverman")
y_expected = 0.76770389927475502
assert_almost_equal(mygauss.covariance_factor(), y_expected, 7)
def test_scott_multidim_dataset(self):
"""Test scott's output for a multi-dimensional array."""
x1 = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
with pytest.raises(np.linalg.LinAlgError):
mlab.GaussianKDE(x1, "scott")
def test_scott_singledim_dataset(self):
"""Test scott's output a single-dimensional array."""
x1 = np.array([-7, -5, 1, 4, 5])
mygauss = mlab.GaussianKDE(x1, "scott")
y_expected = 0.72477966367769553
assert_almost_equal(mygauss.covariance_factor(), y_expected, 7)
def test_scalar_empty_dataset(self):
"""Test the scalar's cov factor for an empty array."""
with pytest.raises(ValueError):
mlab.GaussianKDE([], bw_method=5)
def test_scalar_covariance_dataset(self):
"""Test a scalar's cov factor."""
np.random.seed(8765678)
n_basesample = 50
multidim_data = [np.random.randn(n_basesample) for i in range(5)]
kde = mlab.GaussianKDE(multidim_data, bw_method=0.5)
assert kde.covariance_factor() == 0.5
def test_callable_covariance_dataset(self):
"""Test the callable's cov factor for a multi-dimensional array."""
np.random.seed(8765678)
n_basesample = 50
multidim_data = [np.random.randn(n_basesample) for i in range(5)]
def callable_fun(x):
return 0.55
kde = mlab.GaussianKDE(multidim_data, bw_method=callable_fun)
assert kde.covariance_factor() == 0.55
def test_callable_singledim_dataset(self):
"""Test the callable's cov factor for a single-dimensional array."""
np.random.seed(8765678)
n_basesample = 50
multidim_data = np.random.randn(n_basesample)
kde = mlab.GaussianKDE(multidim_data, bw_method='silverman')
y_expected = 0.48438841363348911
assert_almost_equal(kde.covariance_factor(), y_expected, 7)
def test_wrong_bw_method(self):
"""Test the error message that should be called when bw is invalid."""
np.random.seed(8765678)
n_basesample = 50
data = np.random.randn(n_basesample)
with pytest.raises(ValueError):
mlab.GaussianKDE(data, bw_method="invalid")
class TestGaussianKDEEvaluate:
def test_evaluate_diff_dim(self):
"""
Test the evaluate method when the dim's of dataset and points have
different dimensions.
"""
x1 = np.arange(3, 10, 2)
kde = mlab.GaussianKDE(x1)
x2 = np.arange(3, 12, 2)
y_expected = [
0.08797252, 0.11774109, 0.11774109, 0.08797252, 0.0370153
]
y = kde.evaluate(x2)
np.testing.assert_array_almost_equal(y, y_expected, 7)
def test_evaluate_inv_dim(self):
"""
Invert the dimensions; i.e., for a dataset of dimension 1 [3, 2, 4],
the points should have a dimension of 3 [[3], [2], [4]].
"""
np.random.seed(8765678)
n_basesample = 50
multidim_data = np.random.randn(n_basesample)
kde = mlab.GaussianKDE(multidim_data)
x2 = [[1], [2], [3]]
with pytest.raises(ValueError):
kde.evaluate(x2)
def test_evaluate_dim_and_num(self):
"""Tests if evaluated against a one by one array"""
x1 = np.arange(3, 10, 2)
x2 = np.array([3])
kde = mlab.GaussianKDE(x1)
y_expected = [0.08797252]
y = kde.evaluate(x2)
np.testing.assert_array_almost_equal(y, y_expected, 7)
def test_evaluate_point_dim_not_one(self):
x1 = np.arange(3, 10, 2)
x2 = [np.arange(3, 10, 2), np.arange(3, 10, 2)]
kde = mlab.GaussianKDE(x1)
with pytest.raises(ValueError):
kde.evaluate(x2)
def test_evaluate_equal_dim_and_num_lt(self):
x1 = np.arange(3, 10, 2)
x2 = np.arange(3, 8, 2)
kde = mlab.GaussianKDE(x1)
y_expected = [0.08797252, 0.11774109, 0.11774109]
y = kde.evaluate(x2)
np.testing.assert_array_almost_equal(y, y_expected, 7)
def test_psd_onesided_norm():
u = np.array([0, 1, 2, 3, 1, 2, 1])
dt = 1.0
Su = np.abs(np.fft.fft(u) * dt)**2 / (dt * u.size)
P, f = mlab.psd(u, NFFT=u.size, Fs=1/dt, window=mlab.window_none,
detrend=mlab.detrend_none, noverlap=0, pad_to=None,
scale_by_freq=None,
sides='onesided')
Su_1side = np.append([Su[0]], Su[1:4] + Su[4:][::-1])
assert_allclose(P, Su_1side, atol=1e-06)
def test_psd_oversampling():
"""Test the case len(x) < NFFT for psd()."""
u = np.array([0, 1, 2, 3, 1, 2, 1])
dt = 1.0
Su = np.abs(np.fft.fft(u) * dt)**2 / (dt * u.size)
P, f = mlab.psd(u, NFFT=u.size*2, Fs=1/dt, window=mlab.window_none,
detrend=mlab.detrend_none, noverlap=0, pad_to=None,
scale_by_freq=None,
sides='onesided')
Su_1side = np.append([Su[0]], Su[1:4] + Su[4:][::-1])
assert_almost_equal(np.sum(P), np.sum(Su_1side)) # same energy